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We present the results of an exhaustive study of the ionized gas in NGC 588,a giant H II region in the nearby spiral galaxy M33. This analysis uses a highnumber of diagnostics in the optical and infrared ranges. Four temperaturediagnostics obtained with optical lines agree with a gas temperature of 11000K,while the [O III] 5007/88um ratio yields a much lower temperature of 8000Kapproximately. This discrepancy suggests the presence of large temperatureinhomogeneities in the nebula. We investigated the cause of this discrepancy byconstructing photoionization models of increasing complexity. In particular, weused the constraints from the Halpha and Hbeta surface brightness distributionsand state-of-the-art models of the stellar ionizing spectrum. None of thesuccessive attempts was able to reproduce the discrepancy between thetemperature diagnostics, so the thermal balance of NGC 588 remains unexplained.We give an estimate of the effect of this failure on the O/H and Ne/O estimatesand show that O/H is known to within +/-0.2 dexComment: 20 pages 18 figure

What is the temperature structure in the giant HII region NGC 588?